Question

This prism has a volume of 240 cm3.



What would the volume of the prism be if each dimension was halved? (Scale factor ishttp://static.k12.com/bank_packages/files/media/mathml_68f74329bc2e147090cb3e6f27fbce4255c06f3b_1.gif .)





A.


120 cm3


B.


480 cm3


C.


30 cm3


D.


60 cm3

Answer 1

http://static.k12.com/calms_media/media/395500_396000/395703/2/df976dddee0bcc6657252f77ac772d47dd775716/53252_question.jpg

Answer 2

When you change the side of a solid by a scale factor of k,
the volume changes by a factor of \(k^3\)

Answer 3

Your scale factor is 1/2
What is \((1/2)^3\) ?

Answer 4

idk

Answer 5

We need to find this: \((\dfrac{1}{2}) ^3\)

Have you learned exponents?

Answer 6

For example, what is \(3^2\) ?

Answer 7

18

Answer 8

\[1\frac{ 1 }{ 2 }\]

Answer 9

No, this is how exponents work.

\(3^2 = 3 \times 3 = 9\)

For example,

\(4^3 = 4 \times 4 \times 4 = 64\)

Answer 10

The base tells you which number is going to be multiplied.
The exponent tells you how many of the bases to use.

\(3^2\)

The base is 3, so 3 will be multiplied.
The exponent is 2, so there will be two bases multiplied, or two 3's multiplied.

That means

\(3^2 = 3 \times 3\)

and

\(3 \times 3 = 9\)

so \(3^2 = 3 \times 3 = 9\)

Answer 11

Let's use a higher exponent.

What is 2^4?

You need to multiply four 2's together.

\(2^4 = 2 \times 2 \times 2 \times 2 = 16\)

Answer 12

ok then what

Answer 13

Do you have a better understanding of exponents now?

Answer 14

yes

Answer 15

Ok.
In your problem, the side was changes by a scale factor of 1/2
The rule is if the sides changes by a factor of k, the volume changes by a factor of k^3.

In your case, that means the volume changes by a factor of

\(\left( \dfrac{1}{2} \right)^3\)

Now we need to use our knowledge of exponents and find what

\(\left( \dfrac{1}{2} \right)^3\) is equal to.

Answer 16

\[1\frac{ 1 }{ 2 }\]

Answer 17

According to what the exponents mean,

\(\left( \dfrac{1}{2} \right)^3 = \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2} \)

Answer 18

\[1\frac{ 1 }{ 2 }\]

Answer 19

\(1 \dfrac{1}{2} =
\dfrac{1}{2} + \dfrac{1}{2} +\dfrac{1}{2} \)

We are not adding the fractions. We are multiplying them together.

Answer 20

\(\left( \dfrac{1}{2} \right)^3 = \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2} = \dfrac{1}{2 \times 2 \times 2} = \dfrac{1}{8}\)

Answer 21

o ok

Answer 22

1/8 is quite different from 1 1/2

Answer 23

Ok. Now we know that the volume factor is 1/8 when the side factor is 1/2.
That means that when the side of a solid becomes half what it used to be, the volume becomes 1/8 of what it used to be.

Answer 24

ummm dont get it

Answer 25

If your prism started with a volume of 240 cm^3, and each dimension became half, that means the volume is only 1/8 of 240 cm^3.
What is 240 cm^3 divided by 8 ?

Answer 26

30

Answer 27

Correct.

Answer 28

Here is an explanation with a figure that sometimes makes things easier to understand.

Answer 29

so 30 is the ans